Development of the Bélanger Equation and Backwater Equation by Jean-Baptiste Bélanger (1828)
Publication: Journal of Hydraulic Engineering
Volume 135, Issue 3
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Acknowledgments
The writer acknowledges the helpful comments of Dr. Jerry R. Rogers, University of Houston; Dr. Jerry L. Anderson, University of Memphis; Dr. Glenn O. Brown, Oklahoma State University; Professor Colin J. Apelt, University of Queensland; and Professor John D. Fenton, University of Karlsruhe. He further acknowledges the assistance of the Bibliothèque de l’Ecole Nationale des Ponts et Chaussées, of the Bibliothèque de l’Ecole Centrale de Paris, and of the Archives Municipales de Valenciennes.
References
Bakhmeteff, B. A. (1932). Hydraulics of open channels, 1st Ed., McGraw-Hill, New York.
Bélanger, J. B. (1828). “Essai sur la solution numérique de quelques problèmes relatifs au mouvement permanent des eaux courantes [Essay on the numerical solution of some problems relative to steady flow of water].” Carilian-Goeury, Paris (in French).
Bélanger, J. B. (1841). “Notes sur l’hydraulique [Notes on hydraulic engineering].” Ecole Royale des Ponts et Chaussées, Paris, France, session 1841–1842, 223 pages (in French).
Bélanger, J. B. (1849). “Notes sur le cours d"hydraulique [Notes on a course in hydraulics].” Mém. Ecole Nat. Ponts et Chaussées, Paris, France, session 1849–1850, 222 pages (in French).
Bidone, G. (1819). “Le remou et sur la propagation des ondes [The jump and on wave propagation].” Report to Académie Royale des Sciences de Turin, séance 12 Dec., Vol. XXV, 21–112 & 4 plates (in French).
Boussinesq, J. V. (1877). “Essai sur la théorie des eaux courantes [Essay on the theory of water flow].” Mémoires présentés par divers savants à l’Académie des Sciences, Paris, France, Vol. 23, Série 3, No. 1, supplément 24, 1–680 (in French).
Bresse, J. A. (1860). Cours de mécanique appliquée professé à l’Ecole des Ponts et Chaussées (Course in applied mechanics given at the Pont-et-Chaussées Engineering School.), Mallet-Bachelier, Paris (in French).
Brown, G. O. (2002). “The history of the Darcy-Weisbach equation for pipe flow resistance.” Proc., Environmental and Water Resources History, ASCE 150th Anniversary (1852–2002), J. R. Rogers and A. J. Fredrich, eds., ASCE, Reston, Va., 34–43.
Chanson, H. (1999). The hydraulics of open channel flow: An introduction, Edward Arnold, London.
Chanson, H. (2004). The hydraulics of open channel flow: An introduction, 2nd Ed., Butterworth-Heinemann, Oxford.
Chanson, H. (2006). “Minimum specific energy and critical flow conditions in open channels.” J. Irrig. Drain. Eng., 132(5), 498–502.
Chanson, H. (2007). “Hydraulic jumps: Bubbles and bores.” Proc., 16th Australasian Fluid Mechanics Conference AFMC (CD-ROM), P. Jacobs et al., eds., The University of Queensland, Brisbane QLD, Australia, 39–53.
Chanson, H. (2008). “Jean-Baptiste Charles Joseph Bélanger (1790–1874), the Backwater equation, and the Bélanger equation.” Hydraulic Model Report No. CH69/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia.
Chanson, H. (2009). “Current knowledge in hydraulic jumps and related phenomena. A survey of experimental results.” European J. Mechanics B/Fluids, 28(2).
Chatzis, K. (1995). “Un aperçu de la discussion sur les principes de la Mécanique rationnelle en France à la Fin du Siècle Dernier.” Revue d’Histoire des Mathématiques, 1, 235–270.
Coriolis, G. G. (1836). “Sur l’établissement de la formule qui donne la figure des remous et sur la correction qu’on doit introduire pour tenir compte des différences de vitesses dans les divers points d’une même section d’un courant [On the establishment of the formula giving the backwater curves and on the correction to be introduced to take into account the velocity differences at various points in a cross-section of a stream].” Annales des Ponts et Chaussées, 1st Semester, Series 1, Paris, France, Vol. 11, pp. 314–335 (in French).
Darcy, H. P. G., and Bazin, H. (1865). Recherches hydrauliques (Hydraulic research), Imprimerie Impériales, Paris, 1ère et 2ème Parties (in French).
de Prony, G. C. R. (1804). Recherches physico-mathématiques sur la Théorie des Eaux Courantes (Physical and mathematical research on the theory of water flows), Imprimerie Impériale, Paris (in French).
Froude, W. (1872). “Experiments on the surface-friction experienced by a plane moving through water.” British Association for the Advancement of Science, 42nd meeting, U.K.
Hager, W. H. (1992). Energy dissipators and hydraulic jump, Vol. 8, Water Science and Technology Library, Dordrecht, The Netherlands.
Henderson, F. M. (1966). Open channel flow, MacMillan, New York.
La Houille, Blanche. (1960). “Notre Frontispice. Bélanger (1789–1874).” Houille Blanche, 15(3), 234.
Liggett, J. A. (1993). “Critical depth, velocity profiles, and averaging.” Jl of Irrig., and Drain. Engrg., 119(2), 416–422.
Montes, J. S. (1986). “A study of the undular jump profile.” Proc., 9th Australasian Fluid Mechanics Conference AFMC, Auckland, New Zealand, 148–151.
Montes, J. S. (1998). Hydraulics of open channel flow, ASCE, Reston, Va.
Reech, F. (1852). Cours de mécanique d’après la nature genéralement flexible et elastique des corps, Carilian-Goeury, Paris (in French).
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 135 • Issue 3 • March 2009
Pages: 159 - 163
Copyright
© 2009 ASCE.
History
Received: Jun 1, 2008
Accepted: Oct 23, 2008
Published online: Mar 1, 2009
Published in print: Mar 2009
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